Analysis of Periodically Time-Varying Systems
Many of the practical techniques developed for treating systems described by periodic differential equations have arisen in different fields of application; con sequently some procedures have not always been known to workers in areas that might benefit s
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Editors: A. Fettweis· J. L. Massey· M. Thoma
J. A. Richards
Analysis of Periodically Time¥arying Systems With 73 Figures
Springer-Verlag Berlin Heidelberg New York 1983
J. A. RICHARDS School of Electrical Engineering and Computer Science University of New South Wales P.O. Box 1 Kensington, N.S.W. 2033, Australia
ISBN-13:978-3-642-81875-2
e-ISBN-13:978-3-642-81873-8
DOl: 10.1007/978-3-642-81873-8
Library of Congress Cataloging in Publication Data Richards, John Alan, 1945-. Analysis of periodically time-varying systems. (Communications and control engineering series) Bibliography: p. Includes index. 1. System analysis. I. Title. II. Series. QA402.R47 1983 003 82-5978 AACR2 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to .Verwertungsgesellschaft Wort«, Munich. © Springer-Verlag Berlin, Heidelberg 1983 Softcover reprint of the hardcover 1st edition 1983
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence ofa specific statement, that such names are exempt from tbe relevant protective laws and regulations and therefore free for general use. Typesetting: Asco Trade Typesetting Ltd., Hong Kong 206113020-543210
To Dick Huey
Preface
Many of the practical techniques developed for treating systems described by periodic differential equations have arisen in different fields of application; consequently some procedures have not always been known to workers in areas that might benefit substantially from them. Furthermore, recent analytical methods are computationally based so that it now seems an opportune time for an applications-oriented book to be made available that, in a sense, bridges the fields in which equations with periodic coefficients arise and which draws together analytical methods that are implemented readily. This book seeks to ftll that role, from a user's and not a theoretician's view. The complexities of periodic systems often demand a computational approach. Matrix treatments therefore are emphasized here although algebraic methods have been included where they are useful in their own right or where they establish properties that can be exploited by the matrix approach. The matrix development given calls upon the nomenclature and treatment of H. D'Angelo, Linear TimeVarying Systems: Analysis and Synthesis (Boston: Allyn and Bacon 1970) which deals with time-varying systems in general. It is recommended for its modernity and comprehensive approach to systems analysis by matrix methods. Since the present work is applications-oriented no attempt has been made to be complete theoretically by way of presenting all proofs, existence theorems and so on. These can be found in D'Angelo and classic and well-develope
